Range voting with mixtures of honest and strategic voters

It was conjectured by Range-doubters that
range, while it works well with 100% honest voters,
and also well with 100% strategic voters, might not work so well
with a mixture of the two. The problem would be
if (say) more Bush than Gore voters were strategic, leading
to a huge advantage for Bush.

In the computer simulation experiments below we employed a 50-50 honest-strategic voter mix
(a composition that seems approximately realistic
based on our polling studies) in which each voter chose whether to be honest or
strategic by flipping a coin.
Note: it then is entirely possible in each election
for Bush (or Gore) to get more
strategic voters, and since the number of voters in each election
below was only 61 (not huge) such an imbalance was in fact highly
probable and typical and must have hurtfully
impacted range's Bayesian regret numbers.

As Kevin Venzke put it:

If I don't want to assume that voters will courteously
vote sincerely (even when this limits their power to affect the results),
then I wouldn't use Range, as the result will be rather randomly skewed
based on who chose to exaggerate and who didn't.

So – what happens?
Answer: despite these circumstances, Range still
kicks the butt of all the other ≈50 voting methods available
in our computer sim package IEVS 2.53,
getting the lowest Bayesian regret scores.
In particular, Range is superior to Approval voting (in which all voters
are "forced" by the rules to be strategic, even if they want to be honest),
i.e. what Venzke called "random skewing" actually helped, not hurt.

the
Range+Top2-Runoff method, which actually does better than plain range voting in these
two simulations (albeit in the first one its advantage is statistically insignificant).
That is because range voting can indeed be distorted by strategic voters;
adding a top2-runoff after the range voting election, can partially correct for
that because in a 2-candidate runoff,
even strategic voters will always be honest.
Range2Runoff tends to improve slightly over
plain Range (up to 10-30% regret reduction)
when 75% or more of the voters are strategic. But when 75% or more
of the voters are honest, plain range is better than Range2Runoff
by a lot (up to ≈3 times smaller regret). In view of that, plain Range still appears to
be the best method overall.

No other method of those listed here
(aside from Range2Runoff
and trivial Range variants)
is capable of bettering Range's Bayesian regret by a statistically significant margin
under any simulation parameters so far tried.

Range is more Condorcet than Condorcet methods!

Also note that Range and its variants
(Range2Runoff, Approval2Runoff)
in these simulations with 50% honest voters
actually yield the true-utility-based Condorcet winner more often than any
other method, including "Condorcet methods" shown
colored. That counterintuitive
conclusion was forecast
in a different model of strategic voting than the one simulated here.
(The one here involves voters who believe a priori that
candidate k+1 is far less likely to win
than candidate k, and act accordingly to maximize their vote's impact.)
This is a very strong reason not to prefer Condorcet voting methods over range –
with a 50-50 mix of strategic and honest voters, range actually
does their own job better than they do!

Caveats:
IEVS 2.53 is still an early version and does not contain a lot of voter strategies and utility
generators planned for later IEVS versions and which had been in my old (1999-2000) simulator.
In particular, all rank-order voting methods shown here are strict
rank-order, i.e. with rank-equalities forbidden in ballots. It has been suggested that
variant-methods in which rank-equalities are permitted – especially Condorcet
methods based on the "winning votes" concept –
would handle strategic voters better. That is probably true. If wv-condorcet strategy were
the same as approval-voting (and it definitely is
not, but that might be a semi-decent approximate view)
then in fact range and wv-Condorcet methods would all exhibit
identical Bayesian Regrets with 100% strategic voters, and presumably considerably
closer-than-here-shown
BRs for a 50-50 mix, although I would expect Range still would have better (i.e. smaller) BRs.
Also, in that case, range might no longer be better than Condorcet methods for the purpose
of generating honest-voter Condorcet winners in the presence of strategic voters.
All this, however, has to be regarded as speculation until more advanced
IEVS versions appear that are capable of handling equalities in
rank-order votes.

What if IRV & Condorcet voters are honest more often than range voters?

This objection was raised by one of our critics. We respond

Where is any evidence for that?

Suppose it is so. Suppose Condorcet and IRV voters really are little paragons
of total honesty – angels – while exactly 50% of the range voters
are nasty strategic
exaggerators out to hurt the poor little innocent honest ones (other 50%).
Fine.
To cast light on this we reran the simulation in the green table
with IEVS 3.24 this time for 100% honest voters. (See the second regret column.)
What happened?
As you can see,
the Condorcet methods yield regrets between
0.1127 and 0.1331 (for Black's Condorcet method and UncAAO respectively, which are the
two best Condorcet methods in this run)
and 0.1783 and 0.1821 (for SmithIRV and Raynaud
respectively, which are the two worst Condorcet methods in this run).
And IRV delivered regret=0.2168.
(Error bars are ±0.005 or less.)
Meanwhile range with a mix of 50% honest and 50% strategic voters yielded regret
0.1633, while range+top2runoff yielded 0.1479.
In other words, even then, and even in the situation in the green table designed to maximally
make range voting look bad due to Venzke's "random skewing" effect, range and range+top2runoff still
outperform IRV and perform comparably to Condorcet methods even when the latter two have
angels as voters! (But we suggest to you that, sadly, Condorcet and IRV voters will not actually be angels
who vote 100% honestly.)

Any questions?

Why were the range-doubters wrong?

Two possible ways to look at it:

Range indeed is hurt when honest voters are replaced by strategic ones, but
not enough to kick it out of first place (and/or the other methods
are hurt by strategic voting too, enough to keep them out of first).

The idea that the horrible Bush voters will gain a huge advantage over Gore voters if
there are a larger number of Bush than Gore voters who are strategic,
perhaps is the wrong way to look at it. Perhaps a better way to look at it is:
there are two voter populations: strategic and honest. The strategic ones use
approval voting. (Fine point: strategic and honest approval voting
are notexactly the same thing. They differ slightly.)
The honest ones use
range voting. Then you add up all the votes.
Sure, with only 61 voters (or especially with only 13 voters!), the strategic voter
set will generally be imbalanced and include more Gore than Bush supporters (or the reverse)
– but so what? Approval voting is a pretty good voting system (and it is even better if
some honest range votes are added on). So the results will be pretty good. Meanwhile
non-range systems like Condorcet, IRV, etc, all will have to deal with the same typical
imbalances. The net result is range ends up doing better than them in terms
of Bayesian Regret, which is exactly what these computer
simulations of thousands of elections show. (We also have many, many, more
such simulations, far too many to put on this page. This is just one typical
results-table example, got from the random-normal elections model.
They all behave this way. And you can download IEVS and run it
yourself in different models.) The fact is, fear of the strategic imbalance "bugaboo"
simply is not justified by the evidence once we go beyond intuitive worries
about "fairness" and actually try the experiments.